] We present a constructive link between relativistic kinematics and nonequilibrium thermodynamic state-space dynamics by projecting GENERIC evolution onto a single scalar state variable identified with rapidity. Once this variable parametrizes the unit timelike four-velocity, Minkowski spacetime kinematics-including inertial motion, uniformly accelerated (Rindler) worldlines, and Lorentz-invariant velocity composition-emerge as a geometric embedding rather than a fundamental assumption [1-5]. Constant rates of change of the projected rapidity generate hyperbolic worldlines, while inertial motion arises as the vanishing-acceleration limit, establishing a direct correspondence between abstract state-space dynamics and relativistic motion [3, 4]. This framework provides a natural dynamical interpretation of relativistic radiation processes. Writing the Lorentz factor as γ = cosh θ, we show that the characteristic relativistic beaming angle scales as ∆θcone ∼ sech θ, allowing radiation formation conditions to be expressed directly in terms of rapidity variation [6, 7]. In the appendix, the standard jitter radiation criterion is reformulated as a condition on the projected GENERIC flow: jitter emission occurs when the rapidity change over a formation time satisfies ∆θ form ≳ 1/γ [ \cite{Medvedev_2000} ]. This clarifies that the distinction between jitter and non-jitter radiation is not purely kinematic, but reflects whether radiation probes non-Hamiltonian, entropy-producing components of the underlying state-space dynamics [2, 9]. The final result is a unified picture in which relativistic motion and radiation properties emerge from projected thermodynamic dynamics: smooth, Hamiltonian-dominated rapidity evolution yields conventional synchrotron-or curvature-like emission, while rapid, non-Hamiltonian fluctuations naturally give rise to jitter radiation [6, 8].